I would argue that it is not a fair statement and that the poem is far more concerned with the effects of reason on human beings than it is with the complex emotions implied by the term sensibility.

The speaker of the poem addresses the Christian divine trinity of God, Christ, and the Holy Spirit directly, asking that this "three-person'd God" attack him and take him captive in order to "make [him] new." He wishes to believe without question and to devote himself fully to God, but his faculty of "Reason"—which God gave him—actually prevents him from being able to do so. This is why he asks God to break the bond between the speaker and God's "enemy"—reason, it seems, again—as he loves God and wants to be "betroth'd" to God rather than restrained by his own faulty reason. He entreats God to "imprison" him so that he can never be free from God's love or influence or grace.

If God does not do this work for him, he implies, it will be impossible for him to do it himself because his reason is so overpowering; he needs some proof, it seems, of God's existence. He would be as a slave to God, even suggesting that he cannot be chaste (abstaining from sexual relations) unless God "ravish[es]" the speaker himself. He needs God to fill him up and move him spiritually, as one is moved physically by the act of sex.